H∞ control for continuous-time Takagi–Sugeno fuzzy model by applying generalized Lyapunov function and introducing outer variables

Abstract This paper presents a novel approach to the design of fuzzy state feedback controllers for continuous-time non-linear systems with input saturation under persistent perturbations. It is assumed that all the states of the Takagi-Sugeno (TS) fuzzy model representing a non-linear system are measurable. Such controllers achieve bounded input bounded output (BIBO) stabilisation in closed loop based on the computation of inescapable ellipsoids. These ellipsoids are computed with linear matrix inequalities (LMIs) that guarantee stabilisation with input saturation and persistent perturbations. In particular, two kinds of inescapable ellipsoids are computed when solving a multiobjective optimization problem: the maximum volume inescapable ellipsoids contained inside the validity domain of the TS fuzzy model and the smallest inescapable ellipsoids which guarantee a minimum *-norm (upper bound of the 1-norm) of the perturbed system. For every initial point contained in the maximum volume ellipsoid, the closed loop will enter the minimum *-norm ellipsoid after a finite time, and it will remain inside afterwards. Consequently, the designed controllers have a large domain of validity and ensure a small value for the 1-norm of closed loop.

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Further Study on Observer Design for Continuous-Time Takagi–Sugeno Fuzzy Model With Unknown Premise Variables via Average Dwell Time

IEEE Transactions on Cybernetics ◽

10.1109/tcyb.2019.2933696 ◽

2020 ◽

Vol 50 (11) ◽

pp. 4855-4860 ◽

Cited By ~ 3

Author(s):

Likui Wang ◽

Hak-Keung Lam

Keyword(s):

Continuous Time ◽

Dwell Time ◽

Fuzzy Model ◽

Average Dwell Time ◽

Observer Design ◽

Takagi Sugeno

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ANTICONTROL OF CHAOS FOR A CONTINUOUS-TIME TAKAGI–SUGENO FUZZY SYSTEM VIA LOCAL TIME-DELAY FEEDBACK

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127405014362 ◽

2005 ◽

Vol 15 (12) ◽

pp. 3883-3894 ◽

Cited By ~ 2

Author(s):

TAEK RYONG KIM ◽

YOUNG HOON JOO ◽

JIN BAE PARK ◽

GUANRONG CHEN

Keyword(s):

Time Delay ◽

Discrete Time ◽

Continuous Time ◽

Fuzzy System ◽

Closed Loop ◽

Fuzzy Controller ◽

Design Method ◽

Fuzzy Model ◽

Takagi Sugeno ◽

Systematic Control

In this paper, a simple and systematic control design method is proposed for making a continuous-time Takagi–Sugeno (T–S) fuzzy system chaotic. The concept of parallel distributed compensation is employed to determine the structure of a fuzzy controller from a T–S fuzzy model. The fuzzy controller makes the T–S fuzzy model, which could be stable or unstable, bounded and chaotic. The verification of chaos in the closed-loop T–S fuzzy system is done by the following procedure. First, we establish an asymptotically approximate relationship between a continuous-time T–S fuzzy system with time-delay and a discrete-time T–S fuzzy system. Then, we verify the chaos in the closed-loop T–S fuzzy system by applying the Marotto theorem to its associated discrete-time T–S fuzzy system. The generated chaos is in the sense of Li and Yorke. Two examples are given to show that this methodology is simple and effective for anticontrol of chaos for a continuous-time T–S fuzzy system.

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